Question 894855
p = m / (m+n)


multiply both sides of the equation by (m+n) to get:


p * (m+n) = m


simplify to get:


pm + pn = m


subtract pm from both sides of the equation to get:


pn = m - pm


factor out the m to get:


pn = m*(1-p)


divide both sides of the equation by (1-p) to get:


pn / (1-p) = m


that's your solution


m = pn / (1-p)


you can confirm by giving m and n a value in the original equation and then solve for p.


you can then confirm by giving p and n the same values in the final equation and then solve for m.


your values for m and n and p in both equation should wind up being the same.



for example:


let m = 8 and n = -4 in the original equation.


p = m / (m+n) = 8/(8-4) = 8/4 = 2


you have m = 8, n = -4, and p = 2 in the original equation


now let n = -4 and p = 2 in the final equation.


m = p*n / (1-p) = 2*-4 / (1-2) = -8 / -1 = 8


you have m = 8, n = -4, and p = 2 in the final equation.


you get the same values in both equations.


this confirms the solution is good.